Finite Group Databasebeta

← #11887415

Subgroups — #11887415

Order 1152.

939 conjugacy classes of subgroups.

The subgroup lattice has 839 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5618C211yesmaximal, characteristic, complemented
2#10595018C211yesmaximal, characteristic, complemented
3#10592735C211yesmaximal, characteristic, complemented
4C3×#5041C211yesmaximal, characteristic, complemented
5#10591521C211yesmaximal, characteristic, complemented
6#10591471C211yesmaximal, characteristic, complemented
7#10591449C211yesmaximal, characteristic, complemented
8#10591400C211yesmaximal, characteristic, complemented
9C3⋊C8×#67C211yesmaximal, characteristic, complemented
10#10591132C211yesmaximal, characteristic, complemented
11C2×#63564C211yesmaximal, characteristic, complemented
12#10590610C211yesmaximal, characteristic, complemented
13#10590537C211yesmaximal, characteristic, complemented
14#10590470C211yesmaximal, characteristic, complemented
15#10590425C211yesmaximal, characteristic, complemented
16#83614—31nomaximal
17#80681—31nomaximal
18C22×C4⋊(C3⋊D3)C2211yescharacteristic
19C2×#3799C2211yescharacteristic
20C32×#121C2211yescharacteristic
21C2×#3753C2211yescharacteristic
22C2×#3753C2211yescharacteristic
23C3×#939—21no—
24C3×#938C2211yescharacteristic, complemented
25C3×D4×Dic3—21no—
26C3×D4×Dic3C2211yescharacteristic, complemented
27C2×C3×#214C2211yescharacteristic, complemented
28C3×C4×#67C2211yescharacteristic
29C2×C3×C4⋊Dic3C2211yescharacteristic
30C3×#924C2211yescharacteristic
31C22×C3×C3⋊C8C2211yescharacteristic
32C3×#892C2211yescharacteristic, complemented
33C3×#890C2211yescharacteristic, complemented
34C3×#886—21no—
35C3×#879—21no—
36#63981—21no—
37#63974—21no—
38#63910—21no—
39#63909C2211yescharacteristic
40#63897—21no—
41#63894C2211yescharacteristic
42#63864C2211yescharacteristic
43C2×D3×C3⋊C8C2211yescharacteristic, complemented
44#63657C2211yescharacteristic
45#63636C2211yescharacteristic
46#63636C2211yescharacteristic
47C3×#832C2211yescharacteristic, complemented
48C3×#810C2211yescharacteristic, complemented
49C3×#808C2211yescharacteristic, complemented
50#63576C2211yescharacteristic, complemented
51#63576C2211yescharacteristic, complemented
52Dic3⋊(C3⋊C8)C2211yescharacteristic, complemented
53#63565C2211yescharacteristic, complemented
54#63565C2211yescharacteristic, complemented
55#63564C2211yescharacteristic
56#63564C2211yescharacteristic
57#63564C2211yescharacteristic
58#63564C2211yescharacteristic
59(C2×D3)⋊(C3⋊C8)C2211yescharacteristic, complemented
60Dic3×C3⋊C8C2211yescharacteristic, complemented
61C3×#553—31no—
62#5630—31no—
63#5618D311yescharacteristic, complemented
64#5550—31no—
65C3×#465—31no—
66#5172—31no—
67#5165—31no—
68C2×#821—31no—
69C8×#67—31no—
70#5068—31no—
71#5066—31no—
72#5044—31no—
73#5041D311yescharacteristic, complemented
74#5038—31no—
75#5037—31no—
76#5036—31no—
77#5036—31no—
78#5036—61no—
79#5016—31no—
80C4×#213—31no—
81D4×C3⋊C8—31no—
82#5003—31no—
83#5002—31no—
84#4970—31no—
85C2×#809—31no—
86#4871—31no—
87#4866—31no—
88#4804—31no—
89#4800—31no—
90#4775—31no—
91#4756—31no—
92C23×C3⋊D3—21no—
93C2×C32×D4—21no—
94C2×C32×D4C2311yescharacteristic
95C22×C32×C4C2311yescharacteristic
96C2×C4⋊(C3⋊D3)—22no—
97C2×C4⋊(C3⋊D3)—21no—
98C2×C4⋊(C3⋊D3)—41no—
99C2×C4⋊(C3⋊D3)C2311yescharacteristic
100C2×C4⋊(C3⋊D3)C2311yescharacteristic
101C2×C3×#67—21no—
102C2×C3×#67D411yescharacteristic
103C22×C3×Dic3—21no—
104C22×C3×Dic3—21no—
105C2×C3×C4×D3C2311yescharacteristic
106C2×C3×Dic6C2311yescharacteristic
107C2×#626—21no—
108C2×#626—21no—
109C2×#624—21no—
110C2×#624—21no—
111#3799—22no—
112#3799—41no—
113C32×C4⋊C4C2311yescharacteristic
114C32×C22⋊C4—21no—
115#3753—22no—
116#3753—41no—
117C2×C3⋊(C3⋊C8)C2311yescharacteristic
118C2×C3⋊(C3⋊C8)C2311yescharacteristic
119C3×#217—21no—
120C3×#217—21no—
121C3×#217—21no—
122C3×#217D411yescharacteristic
123C3×#214—41no—
124C3×(C2×D3)⋊C4—21no—
125C3×(C2×D3)⋊C4D411yescharacteristic
126C3×C4⋊Dic3—21no—
127C3×C4⋊Dic3—21no—
128C3×C4⋊Dic3C2311yescharacteristic
129C3×C4⋊Dic3C2311yescharacteristic
130C3×C4⋊Dic3C2311yescharacteristic
131C3×Dic3⋊C4—21no—
132C3×Dic3⋊C4—21no—
133C3×Dic3⋊C4D411yescharacteristic
134C3×C4×Dic3—21no—
135C3×C4×Dic3C2311yescharacteristic
136C2×C3×C3⋊C8—41no—
137C2×C3×C3⋊C8C2311yescharacteristic
138C2×C3×C3⋊C8C2311yescharacteristic
139#3722—21no—
140#3722—21no—
141#3722—21no—
142#3722—21no—
143D3×C3⋊C8—41no—
144#3297—91noSylow
145C2×#239—31no—
146C2×#235—31no—
147C22×D12—31no—
148C22×D12—31no—
149C22×D12—61no—
150C2×C3×SD16—31no—
151C22×C3×C8—31no—
152C3×#126—61no—
153C3×#125—31no—
154C3×#123—61no—
155C3×C22⋊Q8—31no—
156C3×#121—21no—
157C3×#121—31no—
158C3×#121—61no—
159C3×#121C2×D311yescharacteristic
160C3×#121C2×D311yescharacteristic
161C3×C4×D4—31no—
162C3×C4×D4—31no—
163C3×C4×D4—61no—
164C3×#117—31no—
165C2×C3×C4⋊C4—31no—
166#947—31no—
167#939—21no—
168#938C2×D311yescharacteristic, complemented
169#937—61no—
170D4×Dic3—21no—
171D4×Dic3C2×D311yescharacteristic, complemented
172C2×#214C2×D311yescharacteristic, complemented
173C2×#213—31no—
174C2×#213—31no—
175C2×#213—31no—
176C2×#213—31no—
177C2×#213—61no—
178C2×#213—61no—
179#930—31no—
180C4×#67C2×D311yescharacteristic
181C2×C4⋊Dic3C2×D311yescharacteristic
182#924C2×D311yescharacteristic
183C22×C3⋊C8—31no—
184C22×C3⋊C8C2×D311yescharacteristic
185C2×D3×C8—31no—
186#895—31no—
187#895—61no—
188#894—61no—
189#894—61no—
190#893—31no—
191#892C2×D311yescharacteristic, complemented
192#890C2×D311yescharacteristic, complemented
193#886—21no—
194#884—61no—
195#882—61no—
196D3×C22⋊C4—61no—
197D3×C22⋊C4—61no—
198#879—21no—
199#875—31no—
200C4×D12—31no—
201C3×#106—31no—
202C3×#103—31no—
203C3×#102—31no—
204#835—31no—
205#835—31no—
206#832C2×D311yescharacteristic, complemented
207#830—31no—
208#830—31no—
209#830—31no—
210#830—61no—
211#821—31no—
212#821—31no—
213#821—31no—
214#821—31no—
215(C2×D3)⋊C8—31no—
216Dic3⋊C8—31no—
217C8×Dic3—31no—
218#810—31no—
219#810—31no—
220#810C2×D311yescharacteristic, complemented
221#809—31no—
222#809—31no—
223#809—31no—
224#809—31no—
225#809—31no—
226#809—31no—
227#809—31no—
228#809—31no—
229#809—61no—
230#809—61no—
231#808C2×D311yescharacteristic, complemented
232#807—31no—
233#807—31no—
234#807—31no—
235#807—31no—
236C4⋊(C3⋊C8)—31no—
237C4×C3⋊C8—31no—
238C23×C32—21no—
239C23×C32C2×D411yescharacteristic
240C22×C3⋊D3—21no—
241C22×C3⋊D3—21no—
242C22×C3⋊D3—42no—
243C22×C3⋊D3—42no—
244C22×C3⋊D3—81no—
245C22×C3×D3C2×D411yescharacteristic
246C32×D4—21no—
247C32×D4—21no—
248C32×D4—42no—
249C2×C32×C4—21no—
250C2×C32×C4—21no—
251C2×C32×C4—21no—
252C2×C32×C4C2×D411yescharacteristic
253C2×C32×C4C2411yescharacteristic
254C4⋊(C3⋊D3)—21no—
255C4⋊(C3⋊D3)—21no—
256C4⋊(C3⋊D3)—21no—
257C4⋊(C3⋊D3)—42no—
258C4⋊(C3⋊D3)#4112yes—
259C3×#67—22no—
260C3×#67—81no—
261C2×C3×Dic3—21no—
262C2×C3×Dic3—21no—
263C2×C3×Dic3—21no—
264C2×C3×Dic3—21no—
265C2×C3×Dic3—81no—
266C2×C3×Dic3—81no—
267C2×C3×Dic3C2×D411yescharacteristic
268C2×C3×Dic3C2×D411yescharacteristic
269C2×C3×Dic3C2×D411yescharacteristic
270C3×C4×D3—21no—
271C3×C4×D3—21no—
272C3×Dic6—21no—
273C3×Dic6—21no—
274#626—42no—
275#626—81no—
276#624—42no—
277#624—81no—
278C3⋊(C3⋊C8)—21no—
279C3⋊(C3⋊C8)—21no—
280C3×C3⋊C8—21no—
281C3×C3⋊C8—21no—
282#553—31no—
283#546—91no—
284#488—91no—
285#484—91no—
286#482—91no—
287#478—91no—
288#466—91no—
289#465—31no—
290#463—91no—
291#449—91no—
292#447—91no—
293C4×D8—91no—
294C8×D4—91no—
295#416—91no—
296C2×#102—91no—
297C23×D3—61no—
298C23×D3—61no—
299C23×D3—121no—
300C2×C3×Q8—31no—
301C2×C3×D4—21no—
302C2×C3×D4—21no—
303C2×C3×D4—21no—
304C2×C3×D4—31no—
305C2×C3×D4—41no—
306C2×C3×D4—61no—
307C2×C3×D4C22×D311yescharacteristic
308C2×C3×D4C22×D311yescharacteristic
309C22×C3×C4—21no—
310C22×C3×C4—31no—
311C22×C3×C4—61no—
312C22×C3×C4—61no—
313C22×C3×C4C22×D311yescharacteristic
314C22×C3×C4C22×D311yescharacteristic
315C2×#67—21no—
316C2×#67—61no—
317C2×#67—61no—
318C2×#67#6711yescharacteristic
319C22×Dic3—21no—
320C22×Dic3—21no—
321#239—62no—
322#239—121no—
323#235—62no—
324#235—121no—
325C2×D12—31no—
326C2×D12—31no—
327C2×D12—31no—
328C2×D12—31no—
329C2×D12—61no—
330C2×D12—61no—
331C2×D12—62no—
332C2×D12—62no—
333C2×D12—61no—
334C2×D12—61no—
335C2×D12—61no—
336C2×D12—61no—
337C2×D12—122no—
338C2×D12—121no—
339C2×D12—121no—
340C2×D12—121no—
341C2×D12—122no—
342C2×C4×D3—61no—
343C2×C4×D3—61no—
344C2×C4×D3—61no—
345C2×C4×D3—61no—
346C2×C4×D3C22×D311yescharacteristic
347C2×Dic6C22×D311yescharacteristic
348C3×SD16—121no—
349C2×C3×C8—31no—
350C2×C3×C8—31no—
351C2×C3×C8—121no—
352C3×C4⋊C4—21no—
353C3×C4⋊C4—31no—
354C3×C4⋊C4—31no—
355C3×C4⋊C4—31no—
356C3×C4⋊C4—31no—
357C3×C4⋊C4—61no—
358C3×C4⋊C4—61no—
359C3×C4⋊C4—61no—
360C3×C4⋊C4—61no—
361C3×C4⋊C4C22×D311yescharacteristic
362C3×C4⋊C4C22×D311yescharacteristic
363C3×C22⋊C4—21no—
364C3×C22⋊C4—21no—
365C3×C22⋊C4—31no—
366C3×C22⋊C4—31no—
367C3×C22⋊C4—41no—
368C3×C22⋊C4—61no—
369C3×C22⋊C4—61no—
370C3×C22⋊C4—61no—
371C3×C22⋊C4—61no—
372C3×C42—31no—
373C3×C42—61no—
374#217—21no—
375#217—21no—
376#217—21no—
377#217#6711yescharacteristic
378#214—41no—
379#213—62no—
380#213—62no—
381#213—122no—
382#213—121no—
383#213—121no—
384#213—122no—
385(C2×D3)⋊C4—21no—
386(C2×D3)⋊C4—61no—
387(C2×D3)⋊C4—61no—
388(C2×D3)⋊C4—61no—
389(C2×D3)⋊C4—61no—
390(C2×D3)⋊C4—61no—
391(C2×D3)⋊C4—61no—
392(C2×D3)⋊C4—61no—
393(C2×D3)⋊C4—61no—
394(C2×D3)⋊C4#6711yescharacteristic
395C4⋊Dic3—21no—
396C4⋊Dic3—21no—
397C4⋊Dic3C22×D311yescharacteristic
398C4⋊Dic3C22×D311yescharacteristic
399C4⋊Dic3C22×D311yescharacteristic
400Dic3⋊C4—21no—
401Dic3⋊C4—21no—
402Dic3⋊C4#6711yescharacteristic
403C4×Dic3—21no—
404C4×Dic3C22×D311yescharacteristic
405C2×C3⋊C8—31no—
406C2×C3⋊C8—31no—
407C2×C3⋊C8—31no—
408C2×C3⋊C8—31no—
409C2×C3⋊C8—41no—
410C2×C3⋊C8—61no—
411C2×C3⋊C8—61no—
412C2×C3⋊C8—121no—
413C2×C3⋊C8C22×D311yescharacteristic
414C2×C3⋊C8C22×D311yescharacteristic
415D3×C8—121no—
416C22×C32—21no—
417C22×C32—21no—
418C22×C32—41no—
419C22×C32—41no—
420C22×C32—41no—
421C22×C32#13512yes—
422C22×C32C22×D411yescharacteristic
423C2×C3⋊D3—22no—
424C2×C3⋊D3—41no—
425C2×C3⋊D3—41no—
426C2×C3⋊D3—41no—
427C2×C3⋊D3—41no—
428C2×C3⋊D3—41no—
429C2×C3⋊D3—84no—
430C2×C3×D3—21no—
431C2×C3×D3—21no—
432C2×C3×D3—21no—
433C32×C4—21no—
434C32×C4—41no—
435C32×C4C2×#4111yescharacteristic
436C32×C4H(5,𝔽2)11yescharacteristic
437C3×Dic3—21no—
438C3×Dic3—21no—
439C3×Dic3—21no—
440C3×Dic3—41no—
441C3×Dic3—41no—
442C3×Dic3—41no—
443C3×Dic3—41no—
444C2×#41—91no—
445C22×D4—91no—
446C2×SD16—31no—
447C2×D8—91no—
448C2×D8—91no—
449C22×C8—31no—
450C22×C8—91no—
451#126—61no—
452#125—31no—
453#124—91no—
454#123—61no—
455#123—181no—
456C22⋊Q8—31no—
457#121—31no—
458#121—61no—
459#121—91no—
460#121—181no—
461#121D3211yescharacteristic
462#120—181no—
463C4×D4—31no—
464C4×D4—31no—
465C4×D4—61no—
466C4×D4—91no—
467#117—31no—
468C2×C4⋊C4—31no—
469C2×C22⋊C4—181no—
470#107—91no—
471#107—91no—
472#106—31no—
473C4⋊C8—91no—
474#103—31no—
475#103—91no—
476#103—91no—
477#102—31no—
478#102—91no—
479#102—91no—
480#102—91no—
481#102—91no—
482#102—91no—
483#102—91no—
484C22⋊C8—91no—
485C22⋊C8—91no—
486C4×C8—91no—
487C23×C3—21no—
488C23×C3—21no—
489C23×C3—21no—
490C23×C3—31no—
491C23×C3—41no—
492C23×C3D3×D411yescharacteristic
493C23×C3C2×#6711yescharacteristic
494C22×D3—61no—
495C22×D3—61no—
496C22×D3—61no—
497C22×D3—61no—
498C22×D3—121no—
499C22×D3—121no—
500C22×D3—122no—
501C22×D3—122no—
502C22×D3—124no—
503C22×D3—122no—
504C22×D3—122no—
505C22×D3—242no—
506C22×D3—241no—
507C22×D3—241no—
508C22×D3—242no—
509C22×D3C2×#6711yescharacteristic
510C3×Q8—61no—
511C3×Q8—61no—
512C3×D4—21no—
513C3×D4—21no—
514C3×D4—21no—
515C3×D4—21no—
516C3×D4—41no—
517C3×D4—41no—
518C3×D4—42no—
519C3×D4—42no—
520C3×D4—62no—
521C3×D4—82no—
522C3×D4—241no—
523C2×C3×C4—21no—
524C2×C3×C4—21no—
525C2×C3×C4—21no—
526C2×C3×C4—21no—
527C2×C3×C4—21no—
528C2×C3×C4—21no—
529C2×C3×C4—21no—
530C2×C3×C4—21no—
531C2×C3×C4—31no—
532C2×C3×C4—31no—
533C2×C3×C4—31no—
534C2×C3×C4—41no—
535C2×C3×C4—41no—
536C2×C3×C4—41no—
537C2×C3×C4—61no—
538C2×C3×C4—61no—
539C2×C3×C4—61no—
540C2×C3×C4—61no—
541C2×C3×C4—61no—
542C2×C3×C4—61no—
543C2×C3×C4—241no—
544C2×C3×C4—241no—
545C2×C3×C4D3×D411yescharacteristic
546C2×C3×C4C2×#6711yescharacteristic
547C2×C3×C4C23×D311yescharacteristic
548C2×C3×C4C23×D311yescharacteristic
549#67—22no—
550#67—81no—
551#67—122no—
552#67—241no—
553C2×Dic3—21no—
554C2×Dic3—21no—
555C2×Dic3—21no—
556C2×Dic3—21no—
557C2×Dic3—81no—
558C2×Dic3—81no—
559C2×Dic3C2×#6711yescharacteristic
560C2×Dic3C2×#6711yescharacteristic
561C2×Dic3C2×#6711yescharacteristic
562D12—32no—
563D12—32no—
564D12—62no—
565D12—62no—
566D12—61no—
567D12—61no—
568D12—61no—
569D12—61no—
570D12—61no—
571D12—61no—
572D12—121no—
573D12—121no—
574D12—122no—
575D12—122no—
576D12—124no—
577D12—122no—
578D12—241no—
579C4×D3—21no—
580C4×D3—21no—
581C4×D3—122no—
582C4×D3—122no—
583C4×D3—241no—
584C4×D3—241no—
585Dic6—21no—
586Dic6—21no—
587C3×C8—61no—
588C3×C8—61no—
589C3⋊C8—21no—
590C3⋊C8—21no—
591C3⋊C8—61no—
592C3⋊C8—61no—
593C3⋊C8—61no—
594C3⋊C8—61no—
595C3⋊C8—121no—
596C3⋊C8—121no—
597C2×C32—22no—
598C2×C32—81no—
599C2×C32#54611yescharacteristic
600C2×C32C2×#13511yescharacteristic
601C2×C32#57611yescharacteristic
602C3⋊D3—42no—
603C3⋊D3—81no—
604C3×D3—41no—
605C24—181no—
606#41—182no—
607#41—361no—
608C2×Q8—31no—
609C2×D4—21no—
610C2×D4—31no—
611C2×D4—61no—
612C2×D4—91no—
613C2×D4—91no—
614C2×D4—182no—
615C2×D4—181no—
616C2×D4—181no—
617C2×D4—181no—
618C2×D4—361no—
619C2×D4C2×D3211yescharacteristic
620C22×C4—31no—
621C22×C4—61no—
622C22×C4—61no—
623C22×C4—181no—
624C22×C4—181no—
625C22×C4C2×D3211yescharacteristic
626SD16—121no—
627D8—182no—
628D8—361no—
629C2×C8—31no—
630C2×C8—31no—
631C2×C8—91no—
632C2×C8—91no—
633C2×C8—121no—
634C2×C8—361no—
635C4⋊C4—31no—
636C4⋊C4—31no—
637C4⋊C4—31no—
638C4⋊C4—31no—
639C4⋊C4—61no—
640C4⋊C4—61no—
641C4⋊C4—61no—
642C4⋊C4—61no—
643C4⋊C4C2×D3211yescharacteristic
644C22⋊C4—21no—
645C22⋊C4—31no—
646C22⋊C4—31no—
647C22⋊C4—61no—
648C22⋊C4—61no—
649C22⋊C4—61no—
650C22⋊C4—61no—
651C22⋊C4—181no—
652C22⋊C4—181no—
653C22⋊C4—181no—
654C22⋊C4—181no—
655C42—31no—
656C42—61no—
657C22×C3—21no—
658C22×C3—21no—
659C22×C3—21no—
660C22×C3—21no—
661C22×C3—21no—
662C22×C3—22no—
663C22×C3—41no—
664C22×C3—41no—
665C22×C3—41no—
666C22×C3—41no—
667C22×C3—41no—
668C22×C3—41no—
669C22×C3—41no—
670C22×C3—41no—
671C22×C3—61no—
672C22×C3—61no—
673C22×C3—61no—
674C22×C3—81no—
675C22×C3—81no—
676C22×C3—81no—
677C22×C3#91612yes—
678C22×C3#95012yes—
679C22×C3C2×D3×D411yescharacteristic
680C22×C3C22×#6711yescharacteristic
681C2×D3—21no—
682C2×D3—21no—
683C2×D3—21no—
684C2×D3—62no—
685C2×D3—62no—
686C2×D3—122no—
687C2×D3—121no—
688C2×D3—121no—
689C2×D3—121no—
690C2×D3—121no—
691C2×D3—122no—
692C2×D3—121no—
693C2×D3—121no—
694C2×D3—121no—
695C2×D3—121no—
696C2×D3—121no—
697C2×D3—121no—
698C2×D3—241no—
699C2×D3—241no—
700C2×D3—241no—
701C2×D3—241no—
702C2×D3—244no—
703C2×D3—244no—
704C2×D3—248no—
705C3×C4—21no—
706C3×C4—21no—
707C3×C4—21no—
708C3×C4—21no—
709C3×C4—41no—
710C3×C4—41no—
711C3×C4—41no—
712C3×C4—61no—
713C3×C4—61no—
714C3×C4—61no—
715C3×C4—81no—
716C3×C4—121no—
717C3×C4—121no—
718C3×C4—121no—
719C3×C4—121no—
720C3×C4#100411yescharacteristic
721C3×C4D3×#4111yescharacteristic
722C3×C4D3×#4111yescharacteristic
723C3×C4#100911yescharacteristic
724Dic3—21no—
725Dic3—21no—
726Dic3—21no—
727Dic3—41no—
728Dic3—41no—
729Dic3—41no—
730Dic3—41no—
731C32#329711yescharacteristic, complemented, Sylow
732C23—21no—
733C23—31no—
734C23—181no—
735C23—181no—
736C23—362no—
737C23—362no—
738C23—721no—
739C23D3×#6711yescharacteristic
740Q8—61no—
741Q8—61no—
742D4—21no—
743D4—21no—
744D4—42no—
745D4—62no—
746D4—92no—
747D4—181no—
748D4—181no—
749D4—181no—
750D4—241no—
751D4—362no—
752D4—362no—
753D4—721no—
754C2×C4—21no—
755C2×C4—21no—
756C2×C4—21no—
757C2×C4—31no—
758C2×C4—31no—
759C2×C4—31no—
760C2×C4—61no—
761C2×C4—61no—
762C2×C4—61no—
763C2×C4—61no—
764C2×C4—61no—
765C2×C4—61no—
766C2×C4—241no—
767C2×C4—241no—
768C2×C4—362no—
769C2×C4—721no—
770C2×C4D3×#6711yescharacteristic
771C2×C4C22×D3211yescharacteristic
772C8—61no—
773C8—61no—
774C8—181no—
775C8—181no—
776C2×C3—22no—
777C2×C3—22no—
778C2×C3—21no—
779C2×C3—21no—
780C2×C3—21no—
781C2×C3—42no—
782C2×C3—81no—
783C2×C3—81no—
784C2×C3—121no—
785C2×C3—161no—
786C2×C3#561011yescharacteristic
787C2×C3C2×#91611yescharacteristic
788C2×C3#576911yescharacteristic
789C2×C3C2×#95011yescharacteristic
790C2×C3#582911yescharacteristic
791C2×C3#583511yescharacteristic
792D3—41no—
793D3—122no—
794D3—122no—
795D3—242no—
796D3—242no—
797D3—241no—
798D3—241no—
799C22—21no—
800C22—21no—
801C22—41no—
802C22—41no—
803C22—41no—
804C22—61no—
805C22—61no—
806C22—61no—
807C22—182no—
808C22—361no—
809C22—361no—
810C22—361no—
811C22—361no—
812C22—361no—
813C22—724no—
814C22#6393512yes—
815C22C2×D3×#6711yescharacteristic
816C4—21no—
817C4—41no—
818C4—61no—
819C4—61no—
820C4—61no—
821C4—121no—
822C4—121no—
823C4—121no—
824C4—121no—
825C4#6431211yescharacteristic
826C4#6431411yescharacteristic
827C3—21no—
828C3#8068111yescharacteristic, complemented
829C3#8361411yescharacteristic, complemented
830C2—22no—
831C2—81no—
832C2—121no—
833C2—362no—
834C2—721no—
835C2C2×#6393511yescharacteristic
836C2#1059530511yescharacteristic
837C2#1059545611yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#121C22
socleC22×C32C22×D4
hypercenter#121D32
hypocenterC32#3297
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ #121

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C3×#5618C2semidirect
2. #10595018C2semidirect
3. #10592735C2semidirect
4. C3×#5041C2semidirect
5. #10591521C2semidirect
6. #10591471C2semidirect
7. #10591449C2semidirect
8. #10591400C2semidirect
9. C3⋊C8×#67C2semidirect
10. #10591132C2semidirect
11. C2×#63564C2semidirect
12. #10590610C2semidirect
13. #10590537C2semidirect
14. #10590470C2semidirect
15. #10590425C2semidirect
24. C3×#938C22semidirect
26. C3×D4×Dic3C22semidirect
27. C2×C3×#214C22semidirect
32. C3×#892C22semidirect
33. C3×#890C22semidirect
43. C2×D3×C3⋊C8C22semidirect
47. C3×#832C22semidirect
48. C3×#810C22semidirect
49. C3×#808C22semidirect
50. #63576C22semidirect
51. #63576C22semidirect
52. Dic3⋊(C3⋊C8)C22semidirect
53. #63565C22semidirect
54. #63565C22semidirect
59. (C2×D3)⋊(C3⋊C8)C22semidirect
60. Dic3×C3⋊C8C22semidirect
63. #5618D3semidirect
73. #5041D3semidirect
168. #938C2×D3semidirect
171. D4×Dic3C2×D3semidirect
172. C2×#214C2×D3semidirect
191. #892C2×D3semidirect
192. #890C2×D3semidirect
206. #832C2×D3semidirect
220. #810C2×D3semidirect
231. #808C2×D3semidirect
731. C32#3297semidirect
828. C3#80681semidirect
829. C3#83614semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C3×#56182
#105950182
#105927352
C3×#50412
#105915212
#105914712
#105914492
#105914002
C3⋊C8×#672
#105911322
C2×#635642
#105906102
#105905372
#105904702
#105904252
#836143
#806813